Physics, asked by Lavi3864, 1 year ago

a load of 2kg produces an extension of 1mm in a wire of 3m in length and 1mm in diameter. The young's modulus of wire will be? answer is 7.48×10^10 Nm-2

Answers

Answered by shubhamjoshi033
84

The young's modulus of the wire is 7.48 x 10¹⁰ Nm⁻²

Explanation :

The applied load =F = mg = 2 x 9.8 = 19.6 N

diameter = 1 mm = 1 x 10⁻³ m

=> radius = 0.5 x 10⁻³ m

Area , A = 3.14r² = 3.14 x 0.25 x 10⁻⁶

= 0.785 x 10⁻⁶

We know that

stress = FORCE/AREA

= 19.6/(0.785 x 10⁻⁶)

= 24.96 x 10⁶

change in length, ΔL = 1 mm = 10⁻³ m

Length, L  = 3 m

hence strain = ΔL/L

= 10⁻³/3

we know that young's modulus is given by the ratio of stress and strain,

Hence

E = 24.96 x 10⁶/10⁻³/3

= 74.8 x 10⁹

= 7.48 x 10¹⁰ Nm⁻²

Hence the young's modulus of the wire is 7.48 x 10¹⁰ Nm⁻²

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